/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 101 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 101

Use a graphing utility to graph two periods of the function. $$y=3 \sin (2 x+\pi)$$

Short Answer

Expert verified
The graph of \(y=3 \sin (2 x+\pi)\) starts at point \((-\frac{\pi}{2},0)\), has a maximum of 3 units above the x-axis, a minimum of 3 units below the x-axis, with period of \(\pi\), and continues this pattern for two periods.

Step by step solution

01

Identify the Amplitude

The amplitude of a sine function is the absolute value of the coefficient of the sine term. In this case, the amplitude is abs(3) = 3 that is, the graph of the function will reach a maximum of 3 units above the x-axis, and a minimum of 3 units below the x-axis.
02

Identify the Phase Shift and Period

The phase shift is found by solving the equation inside the parentheses for \(x=0\). In this case, \(2x+\pi=0\) which gives a phase shift \(x=-\frac{\pi}{2}\). Function has been shifted to the left by \(\frac{\pi}{2}\). The period of a sine function is \(2\pi\) divided by the absolute value of the coefficient of \(x\) inside the sine function. Therefore, the period of this function is \(\frac{2\pi}{2}=\pi\).
03

Plot the function

Start at the phase shift, which is \(-\frac{\pi}{2}\) and make a point at the amplitude (maximum), 0 (zero-crossing), -amplitude (minimum), and 0 (zero-crossing) every \(\frac{\pi}{4}\) (as the period is \(\pi\)). Plot these points for two periods.
04

Draw the sinusoidal function

Complete the plot by drawing a smooth sine wave through the plotted points, paying attention to the shape of sine curve.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the slant asymptote of $$ f(x)=\frac{2 x^{2}-7 x-1}{x-2} $$ (Section \(2.6, \text { Example } 8)\)

Without drawing a graph, describe the behavior of the basic cosine curve.

In Chapter \(5,\) we will prove the following identities: $$ \begin{aligned} \sin ^{2} x &=\frac{1}{2}-\frac{1}{2} \cos 2 x \\ \cos ^{2} x &=\frac{1}{2}+\frac{1}{2} \cos 2 x \end{aligned} $$ Use these identities to solve. Use the identity for \(\sin ^{2} x\) to graph one period of \(y=\sin ^{2} x\)

Use a graphing utility to graph $$ y=\sin x+\frac{\sin 2 x}{2}+\frac{\sin 3 x}{3}+\frac{\sin 4 x}{4} $$ in a \(\left[-2 \pi, 2 \pi, \frac{\pi}{2}\right]\) by [-2,2,1] viewing rectangle. How do these waves compare to the smooth rolling waves of the basic sine curve?

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\tan \frac{x}{4}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.